In his Ph. D, he has studied the viscoelastic behaviour of rocks in terms of the time-scale invariance of local relaxation processes. The constitutive laws of macroscopic behaviours are extrapolated from the experimental and theoretical studies on the dynamics of microstructures, while he established the phenomenological description of mechanical behaviour of rocks from the viewpoint of the scale invariance or complexity. At first, he derived a constitutive law for viscoelastic behaviour including the nonlinear effect due to damage evolutions based on the irreversible thermodynamics. This model was validated for deformation data of a variety of rocks at high temperatures, and he extrapolated a relation based on the relaxation modulus being a temporal power-law. This implies the viscoelastic behaviour of rocks has a time-scale invariance, and we can apply this power-law to the viscoelastic behaviour ranging from the seismic to geological time-scale. This relation is linked to the empirical creep law with an exponent determined by the deformation mechanisms such as dislocation creep or stress corrosion. Moreover, this time-scale invariance affects various power-law relaxation phenomena (e.g., viscoelastic attenuation, damage evolution of rocks, temporal seismicity patterns, transport properties of crustal fluids, electromagnetic radiation and preseismic magnetizaion). His studies contribute to understanding the fundamentals of crustal and mantle dynamics and to assessing earthquake predictability and hazard.
